Simple question about water pressure in a cylinder

AI Thread Summary
In a vertical cylinder filled with water, the pressure at a depth z is given by the formula p_0 + ρgz, where p_0 is atmospheric pressure. The force exerted on a small ring at depth z is calculated using this pressure, leading to a total force for the entire cylinder. The discussion clarifies that while the downward pressure is calculated, the pressure on the sides of the cylinder is also equal due to the nature of liquids, which exert pressure equally in all directions. This principle is fundamental in fluid mechanics and highlights the importance of understanding basic physics concepts. The conversation concludes with an acknowledgment of the complexity of fundamental physics despite advanced knowledge in other areas.
leviadam
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Hi all,

I was asked today by a friend a simple question but couldn't answer so I'm asking you.
Let's assume we have a vertical cylinder full of water, what is the pressure on the sides of the cylinder?

If it was the pressure downwards it simply L*g*rho but to the sides I'm not sure...

10x a lot,
Adam.
 
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Hi.
The preassure in the cylinder on depth z is p_0+\rho g z, where p_0 is an atmosphere.
The force exerting on a small ring with height dz on depth z inside the cylinder is:
(p_0+\rho g z)2 \pi r dz
For the whole cylinder this force is:
\int_0^L (p_0+\rho g z)2 \pi r dz=2 \pi r L (p_0 + \frac{1}{2}\rho g L)
For the bottom of the cylinder the force is:
(p_0+\rho g L)\pi r^2
 
The force you have calculated is the force downwards.
I'm not sure it is the same answer for the sides of the cylinder.

How is it reasonable that the pressure downwards is the same as the pressure to the sides.

Adam.
 
leviadam said:
The force you have calculated is the force downwards.
I'm not sure it is the same answer for the sides of the cylinder.

How is it reasonable that the pressure downwards is the same as the pressure to the sides.

Adam.
The requirement that pressure be the same in all directions is pretty much part of the definition of "liquid"
 
Ah, now I get it.
It's funny, you can learn QFT and GR but you realize you sometimes have shortage in fundamental physics...

10q very very much.
 
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